\(Cov(X_{j1}, X_{k2})\)  and \(Cov(X_{j2}, X_{k1})\)  can be evaluated immediately. Both of these terms measure the covariance between values on the diagonals of \(\mathbf {X}\) , that is the covariance between the maternally and paternally donated variants of the genome inherited from \(\mathbf {F}\)  and \(\mathbf {M}\) , respectively. These covariances therefore measure the amount of inbreeding in a population, that is the degree to which parents tend to have the same genotype. [1]} quantify these covariances with a coefficient \(r\)  for general populations. With known parents, as in this case, these diagonal values are independent of each other and therefore uncorrelated. This can be confirmed by tedious algebra. Explicitly, \(Cov(X_{j1}, X_{k2}) = Cov(X_{j2}, X_{k1}) = 0\) .
